Related papers: Reminiscences by a student of Langlands

I will share with the reader what I have learned from Richard Stanley and the ways in which he has contributed to research in combinatorics conducted by me and my collaborators.

The last decade has seen a proliferation of mentoring programs that provide high-school students authentic research experiences. Such programs expose students to front-line research, equip them with basic research skills (including coding…

This paper provides interested beginners with an updated and detailed introduction to the field of Intelligent Tutoring Systems (ITS). ITSs are computer programs that use artificial intelligence techniques to enhance and personalize…

This is a survey article on developments in modularity since the proof of Fermat's Last Theorem, with an emphasis on the historical development of the subject rather than any technical details.

We construct the Langlands correspondence for connected reductive groups over finite fields, which we call the finite Langlands correspondence. We discuss also its relation with the categorical local Langlands correspondence.

This book introduces the theoretical description and properties of quantum fluids. The focus is on gaseous atomic Bose-Einstein condensates and, to a minor extent, superfluid helium, but the underlying concepts are relevant to other forms…

These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.

I have the rare experience of being on both sides of the mentor--undergraduate student relationship in the same program (Caltech's Summer Undergraduate Research Fellowship, or SURF, program). In this essay, I will discuss how this…

Large Language Models (LLMs) are advancing quickly and impacting people's lives for better or worse. In higher education, concerns have emerged such as students' misuse of LLMs and degraded education outcomes. To unpack the ethical concerns…

Discussion of "Objective Priors: An Introduction for Frequentists" by M. Ghosh [arXiv:1108.2120]

Discussion of "Objective Priors: An Introduction for Frequentists" by M. Ghosh [arXiv:1108.2120]

PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review…

Large language models (LLMs) have been increasingly applied to a wide range of tasks, from natural language understanding to code generation. While they have also been used to assist in bibliographic recommendation, the hallucination of…

Undergraduates are unlikely to even consider graduate research in Computer Science if they do not know what Computer Science research is. Many programs aimed at introducing undergraduate to research are structured like graduate research…

This thesis is designed to be a self-contained exposition of the neurobiological and mathematical aspects of sensory perception, memory, and learning with a bias towards olfaction. The final chapters introduce a new approach to modeling…

These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…

Recent trends in academics show an increase in enrollment levels in higher education Predominantly in Doctoral programmes where individual scholars institutes and supervisors play the key roles The human factor at receiving end of academic…

This paper gives an overview from the perspective of Lie group theory of some of the recent advances in the rapidly expanding research area of quantum entanglement. This paper is a written version of the last of eight one hour lectures…

We introduce Gluon Time Series (GluonTS, available at https://gluon-ts.mxnet.io), a library for deep-learning-based time series modeling. GluonTS simplifies the development of and experimentation with time series models for common tasks…

Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, knot theory and etc. By applying to physics, these novel…